How could I simplify it, could someone show me step by step?

The congruent figures are rectangles that are ABCD is congruent to JKLM.

Given that,

In the picture we have a graph,

We have to find the congruent figures.

In terms of geometry, congruent means having the same dimensions and form. Figures, angles, and line segments can all be used to demonstrate congruence. If two angles have the same measure, they are said to be congruent. When the corresponding sides and angles of two triangles are equal, two triangles are said to be congruent.

The congruent figures are rectangles that are ABCD is congruent to JKLM.

Therefore, The congruent figures are rectangles that are ABCD is congruent to JKLM.

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The value of the given linear functions are:

5. f(3) = 1

6. f(1) + g(2) = 14

7. g(0) = 11

8. g(2) - f(0) = 22

9. f(-1) - g(3) = 20

10. 2g(-4) = 2

We are given the linear functions:

f(x) = 2x - 5 and

g(x) = |- 3x - 11|

Let us solve one by one:

5. f(3)

Substitute the value of x with 3 in f(x), we will get;

f(3) = 2 * 3 - 5 = 6 - 5 = 1

6. f(1) + g(2)

f(1) = 2 * 1 - 5 = 2 - 5 = -3

g(2) = |- 3 * 2  - 11| = |- 6  - 11| = 17

f(1) + g(2) = -3 + 17 = 14

7. g(0)

g(0) = |- 3 * 0  - 11| = | - 11| = 11

8. g(2) - f(0)

g(2) = |- 3 * 2  - 11| = |- 6  - 11| = 17

f(0) = 2 * 0 - 5 = 0 - 5 = -5

g(2) - f(0) = 17 - (-5) = 22

9. f(-1) - g(3)

f(-1) = 2 * -1 - 5 = -2 - 5 = -7

g(3) = |- 3 * 3  - 11| = |- 9  - 11| = 20

10. 2g(-4)

g(-4) = |- 3 * -4  - 11| = |12  - 11| = 1

2g(-4) = 2 * 1 = 2

Thus, the value of the given linear functions are:

5. f(3) = 1

6. f(1) + g(2) = 14

7. g(0) = 11

8. g(2) - f(0) = 22

9. f(-1) - g(3) = 20

10. 2g(-4) = 2

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Answer:

m = - 3 and c = 26

Step-by-step explanation:

• the diagonals of a rhombus are perpendicular bisectors of each other

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{3}[/tex] x + 5 ← is in slope- intercept form

with slope m = [tex]\frac{1}{3}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3 , then

y = - 3x + c ← is the partial equation of AC

to find c substitute A (5, 11 ) into the partial equation

11 = - 15 + c ⇒ c = 11 + 15 = 26

y = - 3x + 26 ← equation of diagonal AC

with m = - 3 and c = 26

The probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.3 is 0.16%.

The normal distribution is a type of probability function that describes how a variable's values are distributed. Since the majority of the observations cluster around the curve's middle peak, it is symmetric. In both directions, the probability for values of the distribution that are far from the mean.

Given that the fracture strength of tempered glass averages 14.1 (measured in thousands of pounds per square inch) and has standard deviation 2.

We have to determine what is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.3?

We that μ = 14.1 σ = 2 n = 100 δ = 2/√100 = 0.2

This probability is 1 subtracted by the p-value of Z when X = 14.3. So

Z = (x-μ)/σ

By the Central Limit Theorem

Z = (x-μ)/δ

Z = (14.3 – 14.1)/0.2

Z = 0.2/0.2

Z = 1

Z =1 has a p-value is 0.8413

= 1 - 0.8413 = 0.1587

Therefore 0.16% is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.3.

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Answer:

The probility is 10%

Step-by-step explanation:

The amount owed at the end of the 6 years duration is $10865

The given parameters about the compound interest are

Principal Amount, P = $5300

Interest Rate, R = 8%

Time, t = 6 years

To calculate the amount owed, we make use of the following formula

A = P + CI

Where

Compound interest, CI = P(1 + R)^t - P

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

In this question, the formula is given as

A = P(1 + r/n)^nt

Where

n = 12, i.e compounded monthly

Substitute the known values in the above equation

A = 5300 * (1 + 8%/12)^(6*12)

Express 8% as decimal

A = 5300 * (1 + 0.08/12)^(6*12)

Evaluate the sum

A = 5300 * (1.01)^(6*12)

Evaluate the exponent

A = 5300 * 2.05

Evaluate the product

A = 10865

Hence, the value of the amount after 6 years is $10865

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Answer:

Around 3.3%

Step-by-step explanation:

The number of 3point shot made by Marques is 2 and the number of free throws he made is 6

Simultaneous equations are two or more algebraic equations with the same unknown variables and the same value of the variables satisfies all such equations. This implies that the simultaneous equations have a common solution.

If the number of 3points made is x and the number of free throw is y, then

x+y= 8 equation 1

the total points made will be

3x+y= 12 equation 2

subtracting equation 1 from 2

2x = 4

x= 4/2= 2

substitute 2 for x in equation 1

2+y= 8

y= 8-2= 6

therefore the number of 3points shot and free throw made are 2 and 6 respectively.

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The interval for the inequality is (5, ∞].

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

-11m <= -55

Now, solving the inequality

-11m ≤ -55

Divide both side by 11

-11m/ 11 ≤ -55/ 11

-m ≤ -5

m≥ 5

Hence, the interval for the inequality is (5, ∞]

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Answer:

Some things that will be true are, that the pattern will go 124,126,128,ect

Another thing is that 124 is an even number

Step-by-step explanation:

The value of fraction [tex]8\frac{9}{20} -5\frac{7}{12}[/tex] = 2.86.

= [tex]8\frac{9}{20} -5\frac{7}{12}[/tex]

it is in the mixed fraction so write it as unmixed.

= 20*8+9 /20 - 12*5+7 / 12

= 160+9 /20 - 60+7 /12

= 169/20 - 67/12

= 8.45 - 67/12

= 12*8.45 - 67 / 12

= 101.4 - 67 / 12

= 34.4/12

= 344/10/12

= 344/10*12

= 344/120

= 2.86

Therefore the value of fraction [tex]8\frac{9}{20} -5\frac{7}{12}[/tex] = 2.86.

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Answer:

29 feet

Step-by-step explanation:

35 - 6 = 29

The main desk is

29 feet above sea level

Answer: $3,565, she not paying no bills.

Step-by-step explanation:

(x + 2)( x – 2)

A. x2 − 8

B. 3x2 − 14x − y

C. x2 − 4

D. x2 − 2

2. Factor Completely: x2 − 36

A. (x + 6)(x – 6)

B. (x + 6)(x + 6)

C. (x – 6)(x − 6)

D. Prime

3. Factor Completely: 4x2 − 81

A. (4x – 9)(x + 9)

B. (2x + 9)(2x + 9)

C. (2x + 9)(2x – 9)

D. (2x – 9)(2x − 9)

4. Factor Completely: x2 + 16

A. (x + 4)(x + 4)

B. (x + 4)(x – 4)

C. Prime

D. (x – 4)(x − 4)

5. Factor Completely: 2x2 − 18

A. Prime

B. 2(x2 − 9)

C. 2(x + 3)(x – 3)

D. 2(x + 3)(x + 3)

6. Factor Completely: 3x2 − 21

c. Yes ΔCBA is congruent to ΔCDE because satisfying meaning of definition by congruency.

How to rotate a triangle using a single point as center?

Following these steps will allow you to rotate a triangle around a fixed point: To one of the triangle's vertices, draw a line extending from the fixed point. Draw the rotated line by taking the angle measurement from this line at the fixed point.

a. The triangle is rotated by ∠ACE , the ray CA also rotated by ∠ACE. Thus the image of ray CA lines up with CE.

b. The rotated edge of CA is CE, thus the image of A coincides with E.

c. Rotation by ∠ACE using C as center.

  As figure is rotated from ∠C from ΔCBA

⇒ΔCAB ≅ ΔCED

Thus the definition of congruence as that a triangle will be are other triangle if they are congruent

∠CBA ≅ ∠CDE

AC = CD

AB = DE

Yes ΔCBA is congruent to ΔCDE because satisfying meaning of definition by congruency.

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If a park ranger, on top of a 200-­‐foot tower, spots a wolf at an angle of depression of 14°. The distance of the wolf from the base of the tower is:  A. 802.2 ft.

Making use of Tan to solve for x

Let x represent the distance between the tower and the wolf

Hence,

Tan 14° =200/x

Cross multiply

x =  200/Tan 14°

x = 200 / 0.2493

x = 802.2 ft

Therefore the correct option is A.

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The true sentences are:

(a) 7 = 1+2+(-3)+(-4)+5+6

(b) 3 = 1 +(-2)+(-3) +(-4) +5 +6

(c) -1= 1+ 2 + 3 + 4 + (-5) + (-6)

(d) -11= 1 + (-2) + (-3) + 4 + (-5) + (-6)

Two or more expressions with an equal sign are defined as an equation.

(a) The given equation is 7=1?2?3?4?5?6.

7=1?2?3?4?5?6

Insert symbols:

7 = 1+2+(-3)+(-4)+5+6

(b) The given equation is 3=1?2?3?4?5?6.

3=1?2?3?4?5?6

Insert symbols:

3 = 1 +(-2)+(-3) +(-4) +5 +6

(c) The given equation is -1=1?2?3?4?5?6.

-1=1?2?3?4?5?6

Insert symbols:

-1= 1+ 2 + 3 + 4 + (-5) + (-6)

(d) The given equation is -11=1?2?3?4?5?6.

-11=1?2?3?4?5?6

Insert symbols:

-11= 1 + (-2) + (-3) + 4 + (-5) + (-6)

Hence, The true sentences are:

(a) 7 = 1+2+(-3)+(-4)+5+6

(b) 3 = 1 +(-2)+(-3) +(-4) +5 +6

(c) -1= 1+ 2 + 3 + 4 + (-5) + (-6)

(d) -11= 1 + (-2) + (-3) + 4 + (-5) + (-6)

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Answer: 5.4 inches

Step-by-step explanation:

The area of a triangle is the base x height/2.

The red is telling you the triangle is 2.7 inches tall, and the black is telling you that the base is 4 inches.

That means the answer is 4 * 2.7/2 = 5.4

If a line has a slope of -4 and includes the points (-9, -9) and (r, -5), the value of r is 10.5

A line has a slope of -4 and includes the points (-9, -9) and (r, -5)

Slope of a line passing through two points can be calculated by

m =(y₁ - y₂)/(x₁ - x₂)

The point  (-9, -9) be (x₁, y₁ )and (r, -5) be (x₂, y₂)

We need to calculate the value if r

-4 = (-9 - (-5 ))/(-9 - r)

-4 = -4/(-9 - r)

-4 (-9 - r) = -4

38 + 4r = -4

4r = -42

r = 10.5

If a line has a slope of -4 and includes the points (-9, -9) and (r, -5), the value of r is 10.5

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The half-life of sodium-24 is around 15 hours. If just 1/8 of the sodium-24 is left, it has been eliminated in 60 hours.

The half-life is the amount of time needed for half of the initial population of radioactive atoms to decay. T1/2 = 0.693/λ is the equation that describes the connection between the half-life, T1, and the decay constant. The rate of radioactive atoms decaying at any given instant is precisely proportional to the quantity of atoms present at that time, as stated by the radioactive decay law.

dtd N ∝ N

dtd N = λ N

where, N is number of integrated nucleus present in the sample at any time t and λ is decay constant.

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Answer: 12 reams of paper

Step-by-step explanation:

The total number of pages (sheets) necessary is 6000. If a single ream of paper contains 500 sheets, to solve the problem, you need to figure out how many 500s go into 6000. This can be done via division, and therefore,

[tex]6000/500=12[/tex]

Answer:

4d + 5 ≥ 13

Step-by-step explanation:

1. 4d + 5 ≥ 13

-5 -5

4d ≥ 8

4d/4 = d

8/4 = 2

d=2

4x2+5 =13

13≥13

2. 7d - 2 < 12

+2 +2

7d < 14

7d/7= d

14/7 = 2

d=2

7x2-2 = 12

12<12

The solution for the inequality is:

-20 < x < 2

And the graph of the solution set can be seen below.

Here we have the inequality:

|x + 9| - 9 < 2

If we add 9 in both sides, we will get:

|x + 9| < 2 + 9

|x + 9| < 11

Now we can decompose the absolute value in a compound inequality:

-11 < x + 9 < 11

Now we can subtract 9 in the whole inequality to get:

-11 - 9 < x < 11 - 9

-20 < x < 2

The graph of this inequality is the one you can see below.

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Answer:

C. 28

Step-by-step explanation:

-4×(-7)

Open bracket

-4×-7

=28

The required equation of the line is 3x + 2y = 8.

What is an equation?

Algebra is concerned with two types of equations: polynomial equations and the particular case of linear equations. Polynomial equations have the form P(x) = 0, where P is a polynomial, while linear equations have the form ax + b = 0, where a and b are parameters, when there is only one variable. To solve equations from either family, algorithmic or geometric approaches derived from linear algebra or mathematical analysis are used. Algebra also explores and solves Diophantine equations with integer coefficients. The approaches employed are unique and derive from number theory. In general, these equations are complex; one frequently searches just for the existence or lack of a solution, and, if they exist, the number of solutions.

The required equation of the line is

(y-4) = (0+6)/(4-8) (x-0)

or, y - 4 = 6/(-4) x

or, y - 4 = -3/2 x

or, 2y - 8 = -3x

or, 3x + 2y = 8

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The function f(x) = 1/9x² + 12x + 7 has zeros or solution as x = -0.61

Roots of quadratic equation is the values of variables satisfying the given quadratic equation are called its roots. In other words, x = α is a root of the quadratic equation f(x), if f(α) = 0. The real roots of an equation f(x) = 0 are the x-coordinates of the points where the curve y = f(x) intersect the x-axis.

The roots of the quadratic function or zeros of the function is the actual solution of the quadratic function.

In the given function f(x) = 1/9x² + 12x + 7 has roots of -0.608≅ -0.61

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Answer:

All of the above are correct.

Answer:

1<x≤6

Step-by-step explanation:

Subtract 5 from 6 and 5 and 11

$80,000 is subject to a $4433 state income tax.

Taxes are sums of money that citizens are required to pay in accordance with their income, the value of their property, and other factors. These sums of money are used to fund the government's activities. A taxpayer is a natural person, business, or other entity that must pay taxes. The government may provide identity or reference numbers to individuals or businesses as modern taxpayers. One who pays taxes is often referred to as a "taxpayer".

Given,

The sum of the taxes owed in each bracket is the total amount owed in taxes.

2%×$3000 +3%×(8000 -3000) +5%×(17000 -5000) +5.75%×(80000 -17000)

= 60 +150 +600 +3622.5

= $4432.50

≈ $4433

$80,000 is subject to a $4433 state income tax.

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